The elements A and Z combine to produce two different compounds: A2Z3 and AZ2. If .15 mol of A2Z3 has a mass of 15.9g and .15 mole of AZ2 has a mass of 9.3g, what are the atomic masses of A and Z?
Could somebody please help me with this? Can I make a system of equations to solve it, or do I need to do something different? I'm lost. =(
So from the data, you know
.3A+.45Z=15.9
.15A+.30Z=9.3
check my thinking.
Let those atomic masses be A and Z. Here are the two equations you can write:
15.9/0.15 = (2/5)A + (3/5)Z
(Do you see why? 15.9/0.15 = 106 is the molar mass of A2Z3.)
9.3/0.15 = 62 = (1/3)A + (2/3)Z
Rewrite as
530 = 2 A + 3 Z
186 = A + 2 Z
Take it from there.
I think I've got it, thank you!
To solve this problem, you can set up a system of equations using the molar masses of the compounds A2Z3 and AZ2. Let's denote the atomic mass of element A as 'x' and the atomic mass of element Z as 'y'.
First, let's calculate the molar mass of A2Z3. It is given that 0.15 moles of A2Z3 has a mass of 15.9 g. Therefore, the molar mass of A2Z3 can be calculated by dividing the mass by the number of moles:
Molar mass of A2Z3 = 15.9 g / 0.15 mol = 106 g/mol
The molar mass of A2Z3 can also be calculated using the atomic masses of A and Z:
Molar mass of A2Z3 = (2*x) + (3*y)
Similarly, for AZ2, it is given that 0.15 moles of AZ2 has a mass of 9.3 g. Therefore, the molar mass of AZ2 can be calculated as:
Molar mass of AZ2 = 9.3 g / 0.15 mol = 62 g/mol
The molar mass of AZ2 can also be calculated using the atomic masses of A and Z:
Molar mass of AZ2 = x + (2*y)
Now, we can set up a system of equations using the above expressions:
Equation 1: (2*x) + (3*y) = 106
Equation 2: x + (2*y) = 62
To solve this system of equations, you can use any method such as substitution or elimination. Let's solve it using the substitution method:
From Equation 2, we can express x in terms of y:
x = 62 - (2*y)
Now, substitute this value of x in Equation 1:
(2*(62 - (2*y))) + (3*y) = 106
Simplify and solve for y:
124 - 4y + 3y = 106
-y = -18
y = 18
Now substitute the value of y back into Equation 2 to find x:
x + (2*18) = 62
x + 36 = 62
x = 62 - 36
x = 26
Therefore, the atomic mass of element A is 26 and the atomic mass of element Z is 18.